New Operator \(\odot\)

Exam style question: something not seen before

So this is a scary looking question! It introduces a symbol you might never
have seen before, language you might not recognise and it could be hard
to know where to start. Here's a step by step approach to each part of
the question, explaining what needs to be done and why.

Answer:

The \(\odot\) symbol is like a new function. We know what to do when we see \(6\times5\) or \(6+5\) but what do we do when we see \(6\odot5\)?? Well the question tells us;
\[a\odot b = ab + a + b\]
\[6\odot5 = 6\times 5 + 6 + 5 = 41\]
I.
\[x\odot y = xy + x + y = yx + y + x = y\odot x\]
so I. is TRUE